Quantitative ethics

Raoul Grouls

Overview

What could go wrong?

  • data collection
    • biased data
    • measurement errors
    • data quality
  • modelling
    • data preparation
    • assumptions
    • model drift
    • definitions of fairness
  • interpretation
    • simpsons paradox
    • confusing correlation with causation
    • incorrect interpretation
  • application
    • unintended use

Datascience

Data Problems - insufficient quality

timeseries, 3 years monthly data

that’s just 150 datapoints…

solution keep your model as simple as possible

Data Problems - nonrepresentative data

COMPAS algorithm, used in US to predict recidivism for criminals

Algorithm turned out to be racist: Blacks where misclassified twice as much

Cause: a questionnaire was used, in which the bias of society itself was reflected. E.g. both blacks and whites smoke as much marihuana (as can be measured in sewer water), but blacks are 10 times as likely to get a criminal record for this.

solution test for bias on subgroups. Understand simpsons’s paradox.

Data Problems - poor quality

There is a correlation between weatherdata and sales. But the client needs predictions 8 weeks ahead.

How do you get realistic predictions 8 weeks ahead?

Answers:

  1. you don’t

  2. you create a linear regression model that predicts weather 8 weeks ahead

solution be critical towards features. More is not always better. Talk to domain experts.

Data Problems - irrelevant features

If you have 10.000 genes, but only 150 patients and you need to predict 3 types of cancer, you have too much features.

solution prune features, reduce dimensionality, regularize your model

Data Problems - overfitting / underfitting

Symptom: your data performs perfect in training, and fails in real life

Cause: your model is too complex and “memorized” your trainingset.

Question: How big is the observationspace (the number of possible observations) if you have 25 features, each either a 0 or a 1?

Answer: \(2^{25}=3.3 * 10^7\)

solution learn to calculate the size of your searchspace and observationspace

Simpsons paradox

Causal Bayesian Networks

Ethical AI

This is an active area of research. A lot of companies are busy moving their data to the cloud.

When that is done, they often start using algorithms.

And then the question arises: is this fair? And how do we know?

Graphs

We will look at Causal Bayesian Networks.

Networks are represented as a graph. A graph \(G\) is a pair \(G = (V, E)\) where

  • \(V\) is a set of nodes (or points)
  • \(E\) is a set of edges \(\{x, y\}\) with \(x, y \in V\)

Causal Networks

Causal Bayesian Networks are popular tools used by the machine learning community to think about fairness.

The arrow between nodes represent a causal relationship. The Bayesian part means every relationship has an associated probability.

Causal Networks - Example

Assume a college admisision scenario where: students with gender \(G\) are admitted \(A=\{0, 1\}\) based on

  • qualifications \(Q\)
  • choice of department \(D\)

Causal Networks - Example

  • The causal path \(G \to A\) represents a direct influence of gender.
  • The indirect path \(G \to D \to A\) represents that some genders apply more often to certain departments.

Causal Networks - Example

  • \(G \to A\) will be considered unfair
  • \(D \to A\) could be considered fair with respect to college responsibility
  • but \(G \to D\) could be considered unfair with respect to societal responsibility

Causal Networks - Problems

While this might sound very reasonable, and can be a very conscise way of talking about the complex networks of influences, there is an important caveat: the result is not what you would expect it to be.

Causal Networks - Problems

We then show, analytically and empirically, that [causal definitions of fairness] almost always result in strongly Pareto dominated decision policies1

Pareto dominated is a technical way of saying: there is a better choice for everyone involved.

Causal Networks

… policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder

… there is an alternative feasible policy that simultaneously achieves greater student-body diversity and higher college degree attainment

… we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership

Conclusion

The combination of the Simpson’s paradox and the fact that causal definition of fairness result in unfavorable solutions is problematic.

References

Chiappa, S., & Isaac, W. S. (2018, August). A causal Bayesian networks viewpoint on fairness. In IFIP International Summer School on Privacy and Identity Management (pp. 3-20). Springer, Cham.

Nilforoshan, H., Gaebler, J. D., Shroff, R., & Goel, S. (2022, June). Causal conceptions of fairness and their consequences. In International Conference on Machine Learning (pp. 16848-16887). PMLR.